Output feedback stable stochastic predictive control with hard control constraints

TL;DR

This paper introduces a stochastic predictive control method for linear systems with incomplete state information, ensuring stability and bounded control actions through a Kalman filter and specific control policies.

Contribution

It proposes a computationally tractable output feedback stochastic predictive control approach that guarantees mean-square stability for a broad class of linear systems.

Findings

Closed-loop system is mean-square bounded under bounded control actions.

Approach handles incomplete and corrupt observations effectively.

Suitable for large class of linear systems with stochastic stabilization requirements.

Abstract

We present a stochastic predictive controller for discrete time linear time invariant systems under incomplete state information. Our approach is based on a suitable choice of control policies, stability constraints, and employment of a Kalman filter to estimate the states of the system from incomplete and corrupt observations. We demonstrate that this approach yields a computationally tractable problem that should be solved online periodically, and that the resulting closed loop system is mean-square bounded for any positive bound on the control actions. Our results allow one to tackle the largest class of linear time invariant systems known to be amenable to stochastic stabilization under bounded control actions via output feedback stochastic predictive control.